Finite Group Databasebeta

← C2×#11735190 #13521624

Subgroups — C2×#11735190 #13521624

Order 1792.

3550 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6459C211yesmaximal, characteristic
2C22×#6460C211yesmaximal, characteristic
3C22×D7×C4⋊C4C211yesmaximal, characteristic
4C22×#6451C211yesmaximal, characteristic, complemented
5C2×C7×#398C211yesmaximal, characteristic, complemented
6C2×#89761C211yesmaximal, characteristic
7C2×#89751C211yesmaximal, characteristic, complemented
8C2×#89744C211yesmaximal, characteristic, complemented
9C2×#89748C211yesmaximal, characteristic, complemented
10#11735190C2116yesmaximal, direct product factor
11C2×#89440C211yesmaximal, characteristic
12C2×#89439C211yesmaximal, characteristic
13C2×#89433C211yesmaximal, characteristic, complemented
14C2×#89428C211yesmaximal, characteristic, complemented
15C2×#89419C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic
17C23×C4×D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C23×C4×D7C2211yescharacteristic
20C23×Dic14C2211yescharacteristic
21C23×Dic14C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×(C2×D7)⋊C4C2211yescharacteristic
29C22×(C2×D7)⋊C4C2211yescharacteristic
30C22×C4⋊Dic7C2211yescharacteristic
31C22×C4⋊Dic7C2211yescharacteristic
32C22×C4⋊Dic7C2211yescharacteristic
33C22×C4⋊Dic7C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6460—28no—
45C2×#6460C2218yes—
46C2×#6459—28no—
47C2×#6459C2218yes—
48C2×D7×C4⋊C4—28no—
49C2×D7×C4⋊C4C2218yes—
50C2×#6451—28no—
51C2×#6451C2218yescomplemented
52C7×#398C2218yescomplemented
53C2×C7×#95C2211yescharacteristic
54C2×C7×#95C2211yescharacteristic
55C2×C7×#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61#89761C2218yes—
62#89751C2218yescomplemented
63#89748C2218yescomplemented
64#89744C2218yescomplemented
65#89440C2218yes—
66#89439C2218yes—
67#89438C2218yes—
68#89433C2218yescomplemented
69#89428C2218yescomplemented
70#89419C2218yescomplemented
71C2×#2440—71nomaximal, Sylow
72C24×D7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C22×C4×D7—24no—
88C22×C4×D7—24no—
89C22×C4×D7—24no—
90C22×C4×D7—24no—
91C22×C4×D7—24no—
92C22×C4×D7—24no—
93C22×C4×D7—42no—
94C22×C4×D7—42no—
95C22×C4×D7Q818yescomplemented
96C22×C4×D7C2314yes—
97C22×C4×D7C2314yes—
98C22×C4×D7C2314yes—
99C22×Dic14—24no—
100C22×Dic14—24no—
101C22×Dic14—24no—
102C22×Dic14—24no—
103C22×Dic14—42no—
104C22×Dic14—42no—
105C22×Dic14C2314yes—
106C22×Dic14C2314yes—
107C2×C7×C4⋊C4—24no—
108C2×C7×C4⋊C4—24no—
109C2×C7×C4⋊C4—24no—
110C2×C7×C4⋊C4—24no—
111C2×C7×C4⋊C4C2314yes—
112C2×C7×C4⋊C4C2314yes—
113C2×C7×C4⋊C4C2314yes—
114C2×C7×C4⋊C4C2314yes—
115C2×(C2×D7)⋊C4—24no—
116C2×(C2×D7)⋊C4—24no—
117C2×(C2×D7)⋊C4D418yes—
118C2×(C2×D7)⋊C4Q818yescomplemented
119C2×(C2×D7)⋊C4C2314yes—
120C2×(C2×D7)⋊C4C2314yes—
121C2×(C2×D7)⋊C4C2314yes—
122C2×(C2×D7)⋊C4C2314yes—
123C2×C4⋊Dic7—24no—
124C2×C4⋊Dic7—24no—
125C2×C4⋊Dic7—24no—
126C2×C4⋊Dic7—24no—
127C2×C4⋊Dic7C2314yes—
128C2×C4⋊Dic7C2314yes—
129C2×C4⋊Dic7C2314yes—
130C2×C4⋊Dic7C2314yes—
131C2×Dic7⋊C4—24no—
132C2×Dic7⋊C4—24no—
133C2×Dic7⋊C4—24no—
134C2×Dic7⋊C4—24no—
135C2×Dic7⋊C4—24no—
136C2×Dic7⋊C4—42no—
137C2×Dic7⋊C4—42no—
138C2×Dic7⋊C4D418yes—
139C2×Dic7⋊C4C2314yes—
140C2×Dic7⋊C4C2314yes—
141C2×Dic7⋊C4C2314yes—
142C2×Dic7⋊C4C2314yes—
143C2×Dic7⋊C4C2314yes—
144C2×Dic7⋊C4C2314yes—
145C2×Dic7⋊C4C2314yes—
146C2×Dic7⋊C4C2314yes—
147C2×C4×Dic7—24no—
148C2×C4×Dic7—24no—
149C2×C4×Dic7C2314yes—
150C2×C4×Dic7C2314yes—
151#6460—232no—
152#6459—232no—
153D7×C4⋊C4—232no—
154#6451—232no—
155C7×#95C2314yes—
156C7×#95C2314yes—
157C7×#95C2314yes—
158C7⋊#95C2314yes—
159C7⋊#95C2314yes—
160C7⋊#95C2314yes—
161C7⋊#95C2314yes—
162C7⋊#95C2314yes—
163C22×C4⋊Q8—71no—
164C22×C22⋊Q8—71no—
165C22×C22⋊Q8—71no—
166C23×C4⋊C4—71no—
167#2440—716no—
168C2×#398—71no—
169C2×#398D711yescharacteristic, complemented
170C2×#395—71no—
171C2×#395—71no—
172C2×#389—71no—
173C2×#389—71no—
174C2×#385—71no—
175C2×#385—71no—
176C2×#384—71no—
177C2×#380—71no—
178C2×C4×C22⋊C4—71no—
179C24×C7C2411yescharacteristic
180C23×D7—22no—
181C23×D7—22no—
182C23×D7—22no—
183C23×D7—22no—
184C23×D7C2×D414yes—
185C23×D7C2×Q814yes—
186C23×D7C2×Q814yes—
187C23×D7C2412yes—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7C2×D414yes—
206C22×C4×C7C2×D414yes—
207C22×C4×C7C2×Q814yes—
208C22×C4×C7C2×Q814yes—
209C22×C4×C7C2412yes—
210C22×C4×C7C2412yes—
211C22×C4×C7C2412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2412yes—
216C22×Dic7—22no—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7—22no—
221C22×Dic7—22no—
222C22×Dic7—22no—
223C22×Dic7—22no—
224C22×Dic7—22no—
225C22×Dic7—22no—
226C22×Dic7—22no—
227C22×Dic7—22no—
228C22×Dic7—22no—
229C22×Dic7—22no—
230C22×Dic7—22no—
231C22×Dic7C2×D414yes—
232C22×Dic7C2×D414yes—
233C22×Dic7C2×D414yes—
234C22×Dic7C2×Q814yes—
235C22×Dic7C2×Q814yes—
236C22×Dic7#4114yes—
237C22×Dic7C2412yes—
238C22×Dic7C2412yes—
239C22×Dic7C2412yes—
240C22×Dic7C2412yes—
241C22×Dic7C2412yes—
242C22×Dic7C2412yes—
243C22×Dic7C2412yes—
244C2×C4×D7—232no—
245C2×C4×D7—28no—
246C2×C4×D7—28no—
247C2×C4×D7—28no—
248C2×C4×D7—28no—
249C2×C4×D7—28no—
250C2×C4×D7—28no—
251C2×C4×D7—44no—
252C2×C4×D7—44no—
253C2×C4×D7—416no—
254C2×C4×D7—416no—
255C2×C4×D7C2×Q8116yescomplemented
256C2×Dic14—28no—
257C2×Dic14—28no—
258C2×Dic14—28no—
259C2×Dic14—28no—
260C2×Dic14—44no—
261C2×Dic14—44no—
262C2×Dic14—416no—
263C2×Dic14—416no—
264C7×C4⋊C4—28no—
265C7×C4⋊C4—28no—
266C7×C4⋊C4—28no—
267C7×C4⋊C4—28no—
268(C2×D7)⋊C4—28no—
269(C2×D7)⋊C4—28no—
270(C2×D7)⋊C4C2×D4116yes—
271(C2×D7)⋊C4C2×Q8116yescomplemented
272C4⋊Dic7—28no—
273C4⋊Dic7—28no—
274C4⋊Dic7—28no—
275C4⋊Dic7—28no—
276Dic7⋊C4—28no—
277Dic7⋊C4—28no—
278Dic7⋊C4—28no—
279Dic7⋊C4—28no—
280Dic7⋊C4—28no—
281Dic7⋊C4—44no—
282Dic7⋊C4—44no—
283Dic7⋊C4C2×D4116yes—
284C4×Dic7—28no—
285C4×Dic7—28no—
286C23×Q8—71no—
287C23×Q8—71no—
288C24×C4—71no—
289C24×C4—71no—
290C24×C4—71no—
291C2×C4⋊Q8—78no—
292C2×C4⋊Q8—148no—
293C2×C22⋊Q8—78no—
294C2×C22⋊Q8—78no—
295C2×C22⋊Q8—148no—
296C2×C22⋊Q8—148no—
297C22×C4⋊C4—71no—
298C22×C4⋊C4—71no—
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—71no—
304C22×C4⋊C4—71no—
305C22×C4⋊C4—71no—
306C22×C4⋊C4—71no—
307C22×C4⋊C4—71no—
308C22×C4⋊C4—71no—
309C22×C4⋊C4—78no—
310C22×C4⋊C4—148no—
311C22×C4⋊C4C2×D711yescharacteristic
312C22×C4⋊C4C2×D711yescharacteristic
313C22×C4⋊C4C2×D711yescharacteristic
314C22×C4⋊C4C2×D711yescharacteristic
315C22×C22⋊C4—71no—
316C22×C22⋊C4—71no—
317C22×C22⋊C4—71no—
318C22×C22⋊C4—71no—
319C22×C42—71no—
320C22×C42—71no—
321#398—78no—
322#398C2×D718yescomplemented
323#395—78no—
324#395—78no—
325#389—78no—
326#389—78no—
327#385—78no—
328#385—78no—
329#384—78no—
330#380—78no—
331C4×C22⋊C4—78no—
332C2×#95—71no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95C2×D711yescharacteristic
338C2×#95C2×D711yescharacteristic
339C2×#95C2×D711yescharacteristic
340C23×C7C22×D412yes—
341C23×C7C22×D412yes—
342C23×C7C22×Q812yes—
343C23×C7C22×Q812yes—
344C23×C7C2×#4112yes—
345C23×C7H(5,𝔽2)12yes—
346C23×C72−1+412yes—
347C23×C7C2511yescharacteristic
348C22×D7—28no—
349C22×D7—28no—
350C22×D7—28no—
351C22×D7—28no—
352C22×D7—28no—
353C22×D7—28no—
354C22×D7—22no—
355C22×D7—22no—
356C22×D7—22no—
357C22×D7—22no—
358C22×D7C4⋊Q8116yescomplemented
359C22×D7C22×D414yes—
360C22×D7C22×Q814yes—
361C22×D7C22×Q814yes—
362C2×C4×C7—28no—
363C2×C4×C7—28no—
364C2×C4×C7—28no—
365C2×C4×C7—28no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—44no—
384C2×C4×C7—44no—
385C2×C4×C7—44no—
386C2×C4×C7C22×D414yes—
387C2×C4×C7C22×D414yes—
388C2×C4×C7C22×Q814yes—
389C2×C4×C7C22×Q814yes—
390C2×Dic7—28no—
391C2×Dic7—28no—
392C2×Dic7—28no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—44no—
409C2×Dic7—44no—
410C2×Dic7—44no—
411C2×Dic7C22⋊Q8116yescomplemented
412C2×Dic7C22×D414yes—
413C2×Dic7C22×D414yes—
414C2×Dic7C22×D414yes—
415C2×Dic7C22×Q814yes—
416C2×Dic7C22×Q814yes—
417C2×Dic7C2×#4114yes—
418C4×D7—232no—
419C4×D7—416no—
420C4×D7—416no—
421Dic14—416no—
422Dic14—416no—
423C25—71no—
424C22×Q8—74no—
425C22×Q8—74no—
426C22×Q8—144no—
427C22×Q8—144no—
428C22×Q8—144no—
429C22×Q8—144no—
430C22×Q8—282no—
431C22×Q8—282no—
432C23×C4—71no—
433C23×C4—71no—
434C23×C4—71no—
435C23×C4—71no—
436C23×C4—78no—
437C23×C4—74no—
438C23×C4—71no—
439C23×C4—71no—
440C23×C4—71no—
441C23×C4—74no—
442C23×C4—74no—
443C23×C4—144no—
444C23×C4—144no—
445C23×C4—144no—
446C23×C4—144no—
447C23×C4—144no—
448C23×C4—144no—
449C23×C4—282no—
450C23×C4—282no—
451C23×C4C22×D711yescharacteristic
452C23×C4C22×D711yescharacteristic
453C23×C4C22×D711yescharacteristic
454C23×C4C22×D711yescharacteristic
455C23×C4C22×D711yescharacteristic
456C23×C4C22×D711yescharacteristic
457C23×C4C22×D711yescharacteristic
458C4⋊Q8—1432no—
459C22⋊Q8—1432no—
460C22⋊Q8—1432no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—78no—
466C2×C4⋊C4—74no—
467C2×C4⋊C4—74no—
468C2×C4⋊C4—74no—
469C2×C4⋊C4—74no—
470C2×C4⋊C4—74no—
471C2×C4⋊C4—74no—
472C2×C4⋊C4—74no—
473C2×C4⋊C4—74no—
474C2×C4⋊C4—74no—
475C2×C4⋊C4—74no—
476C2×C4⋊C4—74no—
477C2×C4⋊C4—74no—
478C2×C4⋊C4—1432no—
479C2×C4⋊C4—144no—
480C2×C4⋊C4—144no—
481C2×C4⋊C4—144no—
482C2×C4⋊C4—144no—
483C2×C4⋊C4—144no—
484C2×C4⋊C4—144no—
485C2×C4⋊C4—144no—
486C2×C4⋊C4—144no—
487C2×C4⋊C4—144no—
488C2×C4⋊C4—282no—
489C2×C4⋊C4—282no—
490C2×C4⋊C4C22×D714yes—
491C2×C4⋊C4C22×D714yes—
492C2×C4⋊C4C22×D714yes—
493C2×C4⋊C4C22×D714yes—
494C2×C22⋊C4—78no—
495C2×C22⋊C4—78no—
496C2×C22⋊C4—74no—
497C2×C22⋊C4—74no—
498C2×C22⋊C4—74no—
499C2×C22⋊C4—74no—
500C2×C22⋊C4—144no—
501C2×C22⋊C4—144no—
502C2×C42—74no—
503C2×C42—74no—
504C2×C42—144no—
505C2×C42—144no—
506#95—74no—
507#95—74no—
508#95—74no—
509#95—74no—
510#95—74no—
511#95C22×D714yes—
512#95C22×D714yes—
513#95C22×D714yes—
514C22×C7C2×C22⋊Q814yes—
515C22×C7C2×C4⋊Q814yes—
516C22×C7#54414yes—
517C22×C7D4214yes—
518C22×C7#54714yes—
519C22×C7D4×Q814yes—
520C22×C7#55414yes—
521C22×C7C23×D411yescharacteristic
522C22×C7C23×D411yescharacteristic
523C22×C7C23×Q811yescharacteristic
524C22×C7C23×Q811yescharacteristic
525C22×C7C22×#4111yescharacteristic
526C22×C7C2×H(5,𝔽2)11yescharacteristic
527C22×C7C2×2−1+411yescharacteristic
528C2×D7—24no—
529C2×D7—24no—
530C2×D7—24no—
531C2×D7—232no—
532C2×D7—24no—
533C2×D7—24no—
534C2×D7—24no—
535C2×D7C2×C4⋊Q818yescomplemented
536C4×C7—24no—
537C4×C7—24no—
538C4×C7—24no—
539C4×C7—24no—
540C4×C7—42no—
541C4×C7—42no—
542C4×C7—42no—
543Dic7—24no—
544Dic7—24no—
545Dic7—24no—
546Dic7—42no—
547Dic7—42no—
548Dic7—42no—
549Dic7C2×C22⋊Q818yescomplemented
550C24—74no—
551C24—74no—
552C24—74no—
553C24—72no—
554C24—142no—
555C24—142no—
556C24—142no—
557C24—142no—
558C24C23×D711yescharacteristic
559C2×Q8—148no—
560C2×Q8—148no—
561C2×Q8—148no—
562C2×Q8—148no—
563C2×Q8—284no—
564C2×Q8—284no—
565C2×Q8—2816no—
566C2×Q8—2816no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—74no—
585C22×C4—74no—
586C22×C4—74no—
587C22×C4—72no—
588C22×C4—74no—
589C22×C4—74no—
590C22×C4—74no—
591C22×C4—72no—
592C22×C4—72no—
593C22×C4—72no—
594C22×C4—716no—
595C22×C4—72no—
596C22×C4—72no—
597C22×C4—72no—
598C22×C4—148no—
599C22×C4—1432no—
600C22×C4—148no—
601C22×C4—148no—
602C22×C4—148no—
603C22×C4—148no—
604C22×C4—142no—
605C22×C4—142no—
606C22×C4—142no—
607C22×C4—142no—
608C22×C4—142no—
609C22×C4—142no—
610C22×C4—142no—
611C22×C4—142no—
612C22×C4—142no—
613C22×C4—142no—
614C22×C4—142no—
615C22×C4—142no—
616C22×C4—142no—
617C22×C4—142no—
618C22×C4—142no—
619C22×C4—148no—
620C22×C4—284no—
621C22×C4—284no—
622C22×C4—2816no—
623C22×C4—2816no—
624C22×C4D4×D714yes—
625C22×C4D4×D714yes—
626C22×C4Q8×D714yes—
627C22×C4Q8×D714yes—
628C22×C4C23×D712yes—
629C22×C4C23×D712yes—
630C22×C4C23×D712yes—
631C22×C4C23×D712yes—
632C22×C4C23×D712yes—
633C22×C4C23×D712yes—
634C22×C4C23×D712yes—
635C4⋊C4—28no—
636C4⋊C4—28no—
637C4⋊C4—28no—
638C4⋊C4—28no—
639C4⋊C4—716no—
640C4⋊C4—148no—
641C4⋊C4—148no—
642C4⋊C4—148no—
643C4⋊C4—148no—
644C4⋊C4—148no—
645C4⋊C4—148no—
646C4⋊C4—148no—
647C4⋊C4—148no—
648C4⋊C4—148no—
649C4⋊C4—284no—
650C4⋊C4—284no—
651C22⋊C4—716no—
652C22⋊C4—716no—
653C22⋊C4—148no—
654C22⋊C4—148no—
655C42—148no—
656C42—148no—
657C2×C7#244018yescomplemented
658C2×C7C22×C22⋊Q811yescharacteristic
659C2×C7C22×C4⋊Q811yescharacteristic
660C2×C7C2×#54411yescharacteristic
661C2×C7C2×D4211yescharacteristic
662C2×C7C2×#54711yescharacteristic
663C2×C7C2×D4×Q811yescharacteristic
664C2×C7C2×#55411yescharacteristic
665D7—28no—
666C23—716no—
667C23—74no—
668C23—74no—
669C23—74no—
670C23—148no—
671C23—148no—
672C23—148no—
673C23—148no—
674C23—148no—
675C23—148no—
676C23—142no—
677C23—142no—
678C23—142no—
679C23—142no—
680C23C2×D4×D712yes—
681C23C2×D4×D712yes—
682C23C2×Q8×D712yes—
683C23C2×Q8×D712yes—
684C23D7×#4112yes—
685C23#655312yes—
686C23#655412yes—
687C23C24×D711yescharacteristic
688Q8—2816no—
689Q8—2816no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—716no—
715C2×C4—74no—
716C2×C4—74no—
717C2×C4—74no—
718C2×C4—74no—
719C2×C4—74no—
720C2×C4—74no—
721C2×C4—1432no—
722C2×C4—148no—
723C2×C4—148no—
724C2×C4—148no—
725C2×C4—142no—
726C2×C4—142no—
727C2×C4—142no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—142no—
734C2×C4—142no—
735C2×C4—142no—
736C2×C4—142no—
737C2×C4—142no—
738C2×C4—142no—
739C2×C4—142no—
740C2×C4—2816no—
741C2×C4—2816no—
742C2×C4—284no—
743C2×C4—284no—
744C2×C4—284no—
745C2×C4C2×D4×D714yes—
746C2×C4C2×D4×D714yes—
747C2×C4C2×Q8×D714yes—
748C2×C4C2×Q8×D714yes—
749C7C2×#244011yescharacteristic, complemented, Sylow
750C22—78no—
751C22—144no—
752C22—144no—
753C22—144no—
754C22—144no—
755C22—1432no—
756C22—144no—
757C22—144no—
758C22#9030014yes—
759C22D7×C22⋊Q814yes—
760C22#9032314yes—
761C22#9034614yes—
762C22#9038014yes—
763C22#9038114yes—
764C22D7×C4⋊Q814yes—
765C22C22×D4×D711yescharacteristic
766C22C22×D4×D711yescharacteristic
767C22C22×Q8×D711yescharacteristic
768C22C22×Q8×D711yescharacteristic
769C22C2×D7×#4111yescharacteristic
770C22C2×#655311yescharacteristic
771C22C2×#655411yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—78no—
780C4—144no—
781C4—144no—
782C4—144no—
783C4—282no—
784C4—282no—
785C4—282no—
786C2—148no—
787C2#1173519018yesdirect product factor
788C2C2×#9030011yescharacteristic
789C2C2×#9032311yescharacteristic
790C2C2×D7×C22⋊Q811yescharacteristic
791C2C2×#9034611yescharacteristic
792C2C2×#9038111yescharacteristic
793C2C2×#9038011yescharacteristic
794C2C2×D7×C4⋊Q811yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#398C2
socleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#398D7
hypocenterC7C2×#2440
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#398

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C22×#6451C2semidirect
5. C2×C7×#398C2semidirect
7. C2×#89751C2semidirect
8. C2×#89744C2semidirect
9. C2×#89748C2semidirect
10. #11735190C2direct (N × H)
13. C2×#89433C2semidirect
14. C2×#89428C2semidirect
15. C2×#89419C2semidirect
51. C2×#6451C22semidirect
52. C7×#398C22semidirect
62. #89751C22semidirect
63. #89748C22semidirect
64. #89744C22semidirect
68. #89433C22semidirect
69. #89428C22semidirect
70. #89419C22semidirect
95. C22×C4×D7Q8semidirect
118. C2×(C2×D7)⋊C4Q8semidirect
169. C2×#398D7semidirect
255. C2×C4×D7C2×Q8semidirect
271. (C2×D7)⋊C4C2×Q8semidirect
322. #398C2×D7semidirect
358. C22×D7C4⋊Q8semidirect
411. C2×Dic7C22⋊Q8semidirect
535. C2×D7C2×C4⋊Q8semidirect
549. Dic7C2×C22⋊Q8semidirect
657. C2×C7#2440semidirect
749. C7C2×#2440semidirect
787. C2#11735190direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#64592
C22×#64602
C22×D7×C4⋊C42
C22×#64512
C2×C7×#3982
C2×#897612
C2×#897512
C2×#897442
C2×#897482
#117351902
C2×#894402
C2×#894392
C2×#894332
C2×#894282
C2×#894192
C2×#894382
C2×#24407